Erwan Quintin Wisconsin School of Business

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Erwan Quintin Wisconsin School of Business https://mywebspace.wisc.edu/quintin/web/

Transcript of Erwan Quintin Wisconsin School of Business

Page 1: Erwan Quintin Wisconsin School of Business

Erwan QuintinWisconsin School of Business

https://mywebspace.wisc.edu/quintin/web/

Page 2: Erwan Quintin Wisconsin School of Business

Real estate valuation

HEC Paris, 2012

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The question

How should one price real estate assets? Two basic tasks:

1. Describe the distribution of payoffs (i.e. forecast)2. Price that distribution

Arbitrage principle: “similar” assets should be priced in such a way that they earn similar returns

Otherwise…

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Arbitrage opportunities

Paris NYC

Asset

$90M $100M

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Opportunity cost of capital

Investing in a given asset is foregoing the opportunity to invest in other assets with similar properties

Investor should be compensated for foregoing that opportunity

Asset under consideration, therefore, should yield at least the same return (IRR) as other similar assets

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IRRs

The IRR is the discount rate that makes the present value of expected cash flows equal to the initial investment cost

There is only one correct way to compute an IRR:1. Compute expected cash flows2. Find the discount rate that makes the investment’s

net present value zero

Reversing these steps is a typical and massive mistake

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IRRs: warm-up example

An asset pays $500 in year1, and a random cash-flow in year 2

Year 2 CF is $500 with probability p, 0 otherwise

Expected second year CF is 500 p + 0 (1-p)= 500p

Bond’s IRR solves 900=500/(1+r) +500p/(1+r)2

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A deeper example: waterfall structures

Often, real estate projects include several equity holders

Some simply fund the project, others have a hand in running it

Equity can be split simply according to initial stake

Split can also be conditional on performance to give the right incentives to managing stake-holders

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The IRR look-back model

Initial equity injection: $1M,10% managing owner, 90% pension fund

Equity flows are 10% of initial injection in year 1, grow by 10% every year after that. In year five, reversion flow to equity is 10 times year 6 projected cash flow.

Managing owners gets:1. 10% of net equity flows until 10% “hurdle” IRR is reached by

the pension fund (Tier 1)2. 20% of remaining cash flows until 15% IRR is reached by the

pension fund (Tier 2)3. 50% thereafter (Tier 3 cash flows a.k.a the gravy train)

What are cash flows to both equity holders? What is the IRR of both equity holders? Who benefits the most from higher growth rates?

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Main asset pricing recipes

1. Discounted cash flow approacha. Write asset as a string of expected cash flowsb. Find the IRR similar assets earnc. Discount cash flows using that rate

2. Ratio/Peer Group/Multiple approacha. Find a set of similar assets, with known valueb. Find average value/key statistic ratioc. Apply that ratio to asset under consideration

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The multiple approach in real estate

Find a group of comparable properties (‘Comps’) with known value

Comparable: similar location, purpose, vintage…

Compute average ratio of value to gross rental income (Gross Rent Multiplier approach)

Compute average ratio of Net Operating Income (NOI) to value, a key ratio known as the Capitalization Rate

Get an estimate of the current Gross Rent and NOI for your target property, and apply ratio

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Example

A target property has a NOI of $400,000 You have obtained the following two recent sales

data:

NOI Selling price Property 1 $424,200 $4,200,000 Property 2 $387,200 $3,400,000

What is the estimated value of your target using the cap rate approach (assign equal weights to the two sales)?

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Solid comp case in Real Estate

1. Quality of the comparables

2. Consistency of calculations

3. Good treatment of outliers

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Sources for real estate comps/multiples

1. Databases of recent transactions: RCA analytics, Costar

2. Survey data3. “Fundamentals”

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NOI vs. EBITDA

NOI = operating income - operating expenses

Like EBITDA, a fuzzy notion

My preference is to figure cash operating expenses only, making my NOI equivalent to “Normalized EBITDA”

But not everybody agrees…

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NOI vs. PBTCF

NOI = Income net of operating expenses

BT bottom line = NOI – Capital Expenses= Property Before Tax Cash

Flow= PBTCF

Before-tax IRR is the discount rate that makes the PV of all future PBTCF equal to the property’s price

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The holy trinity of real estate

Consider a property with current PBTCF cap rate y%

Assume that PBTCF is expected to grow by g% for ever

Then the before-tax IRR associated with buying this property is:

r = y + g

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Cap rate “fundamentals”

NOI yield ≈ required return (r) - expected income growth (g) + investment rate (CAPEX/V)

Required return = real risk-free rate + expected inflation

+ risk premium + liquidity premium

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Example: Is Manhattan office overvalued?

Cap rates on Manhattan office have fallen back to pre-crisis levels

Could spell trouble, but…

…PwC survey (Q4-2011) is consistent with current valuations:

Required return (r) 7.58%- Cap rate (PBTCF or NOI?) - 5.38%- (Rent growth – Expense growth) (g) - 2.29%

≈ 0

… and spreads over treasuries have actually risen

… though not as much as in other markets

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Cap rates in Manhattan Office

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Cap rates in Manhattan Office

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The class of real estate assets

Bedrock: real estate properties (land + structures affixed to it)

Residential (deliver housing services) or Commercial (held for a business purpose)

Real estate properties are strings of cash flows

Real estate assets are all assets whose payoffs derive -- however remotely -- from some underlying property

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Some language

Debt: financial contract that gives specific claims to asset’s payoff, but no ownership rights

Equity: financial contract that gives only a residual (or subordinated) claim to asset’s payoff, but carries ownership rights

Public Markets: Markets with many buyers and sellers, observable transaction prices and sizes, and stringent disclosure rules

Private Markets: Markets where transactions involve limited numbers of buyers and sellers, and where transaction information and financials need not be disclosed

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Public Markets

Private Markets

Equity Assets

REITsMutual funds

Real PropertiesPrivate investment firms

Debt Assets Mortgage-backed

securities

Whole mortgagesVenture debt

Real estate assets

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REITs (SIICs)

Real Estate Investment Trusts1. buy, sell and hold real estate assets on behalf of a diffuse

shareholder base2. manage these and other assets3. are not taxed at the corporate level

Three basic types: equity, mortgage, hybrid

Can be public or private

UPREITs (U for “umbrella”) hold positions in corporations that invest in real estate, including other REITs

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Brief history

REIT act, 1960: REITs may be treated as untaxed, pass-through entities provided they satisfy a number of requirements

Current requirements include:1. 75% of holdings in RE, cash, or US paper2. 75% of income must come from rents, dividends, mortgage interest, gains

from the sale of qualifying assets or holdings in other REITs3. 90% of taxable income must be distributed to shareholders*4. At least 100 shareholders5. Top 5 holders cannot hold more than 50% of shares

1986 tax reform removed two big downsides of REIT structure:1. Management activities were severely restricted2. Other forms of incorporations (LPs, especially) enjoyed preferential

depreciation rules

1991 Kimco Realty IPO ushered in a new era for REITs

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Market capitalization of Public REITs

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Historical 12-month returns (e-REITs)

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Mortgage-backed securities

Basic idea:1. Pool a large number of mortgages2. Sell the pool as a security, or use the pool as

collateral for one or more debt instruments (bonds)

Purpose:1. Allow more investors to invest in real estate debt

instruments 2. Make that investment more liquid3. Pool/fine-tune risk

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A machine to generate AAA paper

Why did securitization take off after 2000? Among other things because AAA paper became scarce

largely due to the global saving glut (US paper hogs) AAA paper lubricates many key markets, the repo market in

particular Where to find it? There is, after all, only so many blue chip

issuers Answer: CMOs Housing boom created endless supply of mortgages, only

trick is to somehow issue safe bonds backed by unsafe assets

Sounds crazy, but it “works”: no AAA tranche of any CMO deal has defaulted to date (many have been downgraded, but none have formally defaulted)

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The subordination theorem(s)

Theorem1: Risk-free debt can be written against a pool if and only if the worst-case scenario CF realization from the pool is strictly positive

Proof: Let A be the lowest possible CF realization associated with the pool. Make the quantity of debt small enough that the promise is A or less.

Theorem II: Debt with less than a probability p of default can be written against a pool if and only if the CF realization is strictly positive with probability 1-p

Proof: Let A be such that P(CF>A) > 1-p. Make the quantity of debt small enough that the promise is A or less.

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How about them CDOs and CDO2s? Junior tranches of MBS are often pooled into new

deals, often out of necessity (investors won’t pay much for stand-alone B tranches)

If combining these tranches raises the lower bounds on overall cash-flows, more AAA paper can be produced with the right level of credit support

The problem: getting the level of credit support right

Top tranches of many CDO deals defaulted, which means that people overestimated the ability of pooling to dissipate systematic risk

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The game investment banks play

If you get the following trivial point, you understand securitization better than most people who say they understand securitization

Given a pool of assets, investment banks choose a feasible security scheme E to write against a given pool of assets to solve:

Max MV(E) – C(E)

where MV(E) is the market value of scheme E given investors’ willingness to pay for various type of assets while C(E) is the cost of issuing that combination of securities and funding the assets

After 2000, the scope of securitization widened markedly to include riskier pools of assets because the willingness to pay for top tranches made deals profitable that weren’t before

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Mortgage securitization: a short history

The US government wanted liquid secondary markets for mortgages after the great depression: FNMA (1938), GNMA (1968), FHLMC (1970)

Ginnie issues first pass-through in 1968 Bank of America issues first private label

pass-through in 1977 Solomon Brothers and First Boston create

the CMO concept in 1983

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Real estate swap

Two parties exchange (risky) return from some real estate asset for a fixed return

At origination, fixed rate is set so that the value of the swap is zero

As time goes by, swap value rises or falls (symmetrically for the two counterparties)

Swaps are traded in secondary markets, where investors can buy or sell exposure to real estate payoffs…

…without the underlying asset being much involved

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Real estate swap (continued)

In practice, RE swaps involve returns on large indices such as NCREIF, for various subtypes of institutional properties

Institutional Properties: large, safe, premium quality properties in which institutional investors invest

Say you own lots of properties; to offset the risk associated with your investment, you sell the NCREIF return to Credit Suisse for a safe return

Hedge vs. systematic real estate risk

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Market has yet to take off

Four possible explanations:1. No NCREIF forwards2. A redundant asset3. “Liquidity begets liquidity”4. Tough to price

More success in Europe with IPD instruments

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Credit-default swap (CDS)

Protection buyer owns asset subject to default (a MBS, say)

Pays protection seller (AIG, say) fixed premia Seller covers default risk Perfect way to eliminate diversifiable risk Systematic risk remains, however Real-estate related CDS played a big role in

the recent financial mess

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Pricing a revenue-generating property

Consider a property made of a collection of leasable units

How much should a given investor pay for such a property?

Two approaches:1. DCF method (forecast expected flows, discount them)2. Ratio approach (cap and GRM)

Both approaches require detailed cash flow data

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Three levels of cash-flows

Before tax cash flows accrue to:1. Taxes (income and capital gains)2. Debt holders3. Equity holders

After tax cash flows accrue to:1. Debt holders 2. Equity holders

Equity after tax cash flows accrue to equity holders

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Three appropriate discount rates

Before tax cash flows should be discounted at before-tax WACC

After tax cash flows should be discounted at WACC

Equity after tax cash flows should be discounted at required return on equity

First two calculations give the value of the firm, the last one gives the value of equity

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Cash flow pro-forma

Table of expected cash flows associated with the property over a certain horizon

Typical horizon: 5 to 10 years, yearly data

We will first ignore the potential role of debt and taxes, and focus on before tax cash flows

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Potential gross income

Potential Gross Income (PGI): revenue when occupancy is full

PGI = Capacity (in sq. ft) x Expected Rent/Sq. Ft.

Second element requires market trend analysis

Best to go unit by unit and lease by lease to forecast expected rent/sq. ft.

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How to project rents

Forecast market rents:1. Assume a constant growth rate for market rents

(CPI, or average growth rate over recent period)2. Use econometric model to forecast rent growth

Unit-by-unit, use current rent as long as leased, use projected market rent when lease expires, adjusted for unit-specific information

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A typical econometric model (GM 6)

Rents reflect supply and demand Supply at date t: St= St-1 + Ct

Ct is the number of new units on the market at date t St= s(St-1, Rt-k) where k is construction lag Dt= d(Dt-1, Rt, Nt) where Nt is a list of demand drivers Vacancy rate: 0 if Dt>St , (St-Dt)/St otherwise Rt+1=r(Rt , (St-Dt)/St ) 1) Estimate/calibrate r, s and d 2) Forecast Nt , and you’re done

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The real estate cycle

1. Market Value exceeds Replacement Cost2. Investment boom3. Vacancies rise, rents fall, market value falls

below replacement cost4. Supply only responds with a lag5. Vacancy and rents bottom out6. Until market value exceeds replacement cost7. And on we go

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“Fitting is sh%%%ing.”

Edward C. Prescott, Nobel Prize Economist

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Warning

Designing a model that fits historical evidence is trivial

Forecasting is tough More complex models fit better, but forecast

poorly (Wiki “overfitting”) Only criterion that matters: out-of-sample

forecasting fit In other words, how has your forecast

performed? Truth: beating naïve models is tough, and naïve

models are free

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Vacancy allowance

Vacancy allowance = PGI lost to vacancy

Effective Gross Income (EGI) = PGI –Vacancy allowance

Sources: past information, and market analysis

Best to go unit by unit to reflect their specific features, and, obviously, lease length

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Operating expenses

Cost of operating the building: labor, utility bills, property taxes, simple maintenance…

Can be fixed (independent of occupancy) or variable (increasing with occupancy)

Distinguishing features of operating expenses: frequent, mostly predictable and regular

Building betterment investment are not operating expenses

Leases specify who bears what cost and, sometimes, expense stops

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A taxonomy of leases: gross vs. net

Gross lease: owner pays all operating expenses

Net lease: tenant is responsible for at least some operating expenses

Triple net (NNN) lease: all operating expenses are paid by the tenant (EGI+non-rent income≈NOI)

Lease with expense stop: landlord pays operating expenses up to a certain amount, tenant pays the rest

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A taxonomy of leases: types of rent

Flat rent: rent is constant until lease ends

Graduated rent: rent increases on a fixed schedule

Revaluated rent: rent reappraised periodically by an independent professional

Indexed rent: rent is indexed to public index such as CPI

Percentage lease: rent is fixed component (base rent) plus fraction of tenant’s net income or sales

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Net operating income

NOI=PGI – Vacancy Allowance+ Other Income – Operating Expense

Other income = net income from non-rent activities (e.g. laundry machines)

Operating income for the property

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Capital expenditures

Infrequent expenditures, typically though not always meant to better or add to the property (building improvements, leasing commissions…)

Expenses not associated with basic operation

They are cash outflows, and matter for the bottom line

Tax treatment of capital expenditures differs from treatment of operating expenses

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Property before tax cash flow

PBTCF= NOI - Capital expenditures

Expected inflows minus expected outflows

Cash flows to be distributed across three types of stake-holders: 1. Equity holders2. Debt holders3. The tax man

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Reversion cash flows

Reversion cash flows are the result of selling all or part of the property

In most cases, one big reversion cash flow in the last year of the analysis, equal to the expected value of the property at that time, net of transaction costs

Two methods:1. Guess a perpetual rate of growth of PBTCF and discount

the perpetuity at appropriate rate2. Use multiple approach (guess year 11 NOI or EGI, and

apply standard multiple)

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Typical Pro Forma Items

Operating (all years):Potential Gross Income = (Rent*SF) = PGI- Vacancy Allowance = -(vac.rate)*(PGI) = - V+ Other Income = (eg, parking, laundry) = +OI- Operating Expenses = - OE_____________________ _______Net Operating Income = NOI- Capital Expenditures = - CE_____________________ _______Property Before-tax Cash Flow = PBTCF

Reversion (last year & yrs of partial sales only):Property Value at time of sale = V- Selling Expenses = -(eg, broker) = - SE__________________ ______Property Before-tax Cash Flow = PBTCF

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Exhibit 11-2: The Noname Building: Cash Flow Projection

Year: 1 2 3 4 5 6 7 8 9 10 11 Item:

Market Rent/SF: $10.00 $10.10 $10.20 $10.30 $10.41 $10.51 $10.62 $10.72 $10.83 $10.94 $11.05 Potential Revenue: Gross Rent Space 1 (10000SF) $105,000 $105,000 $105,000 $103,030 $103,030 $103,030 $103,030 $103,030 $108,286 $108,286 $108,286 Gross Rent Space 2 (10000SF) $100,000 $100,000 $100,000 $100,000 $100,000 $105,101 $105,101 $105,101 $105,101 $105,101 $110,462 Gross Rent Space 3 (10000SF) $100,000 $101,000 $101,000 $101,000 $101,000 $101,000 $106,152 $106,152 $106,152 $106,152 $106,152 Total PGI $305,000 $306,000 $306,000 $304,030 $304,030 $309,131 $314,283 $314,283 $319,539 $319,539 $324,900

Vacancy allowance: Space 1 $0 $0 $0 $51,515 $0 $0 $0 $0 $54,143 $0 $0 Space 2 $0 $0 $0 $0 $0 $52,551 $0 $0 $0 $0 $55,231 Space 3 $100,000 $0 $0 $0 $0 $0 $53,076 $0 $0 $0 $0 Total vacancy allowance $100,000 $0 $0 $51,515 $0 $52,551 $53,076 $0 $54,143 $0 $55,231

Total EGI $205,000 $306,000 $306,000 $252,515 $304,030 $256,581 $261,207 $314,283 $265,396 $319,539 $269,669 Other Income $30,000 $30,300 $30,603 $30,909 $31,218 $31,530 $31,846 $32,164 $32,486 $32,811 $33,139 Expense Reimbursements Space 1 $0 $1,833 $2,003 $0 $1,651 $964 $1,118 $2,870 $0 $1,823 $329 Space 2 $0 $2,944 $3,114 $1,814 $3,465 $0 $153 $1,905 $469 $2,292 $0 Space 3 $0 $0 $170 $0 $260 $0 $0 $1,752 $316 $2,139 $645 Total Revenue $235,000 $341,078 $341,891 $285,238 $340,624 $289,075 $294,324 $352,974 $298,667 $358,602 $303,781

Reimbursable Operating Expenses

Property Taxes $35,000 $35,000 $35,000 $35,000 $35,000 $36,750 $36,750 $36,750 $36,750 $36,750 $36,750 Insurance $5,000 $5,000 $5,000 $5,000 $5,000 $5,250 $5,250 $5,250 $5,250 $5,250 $5,250 Utilities $16,667 $25,500 $26,010 $22,109 $27,061 $23,002 $23,462 $28,717 $24,410 $29,877 $25,396 Total Reimbursable Expenses $56,667 $65,500 $66,010 $62,109 $67,061 $65,002 $65,462 $70,717 $66,410 $71,877 $67,396 Management Expense $6,150 $9,180 $9,180 $7,575 $9,121 $7,697 $7,836 $9,428 $7,962 $9,586 $8,090 Total Operating Expenses $62,817 $74,680 $75,190 $69,684 $76,182 $72,699 $73,298 $80,146 $74,371 $81,463 $75,486

NOI $172,183 $266,398 $266,701 $215,554 $264,442 $216,376 $221,026 $272,828 $224,295 $277,139 $228,295

Capital Expenditures TI $50,000 $50,000 $55,000 $55,000 $55,000 $55,000 Leasing Commissions $15,150 $15,455 $15,765 $15,923 $16,243 $16,569 Common physical improvements

$100,000

Net Cash Flow (operations) $172,183 $201,248 $266,701 $150,100 $164,442 $145,611 $150,103 $272,828 $153,053 $277,139 Net Cash Flow (reversion) $2,282,951

IRR @ $2,000,000 price: 10.51%

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Going in IRR

Given a proposed property price, and a full pro-forma, a “total” IRR can be calculated

It is the discount rate that makes the present value of all expected PBTCF equal to the price

A sound decision rule: compute typical IRR on similar properties, and take project if property IRR exceeds this typical IRR

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Equivalently, use the DCF method

Estimate required return on similar property (the opportunity cost of capital)

Discount PBTCF at rate

Another sound decision rule: accept project if resulting value exceeds the price

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Typical returns: real estate indices

NCREIF property index (NPI) Survey Cap rate approach (holy trinity) Asset pricing models

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Real estate returns: indices

NCREIF property index (NPI): “quarterly … total rate of return measure … of a very large pool of individual commercial real estate properties. …acquired, at least in part, on behalf of tax-exempt institutional investors”

Return ≈ (NOI + capital gains)/(Initial market value)

“Class A”, premium, institutional quality properties

Europe and other non-US OECD: IPD

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Two big issues with real estate indices

Coverage: institutional properties (owned directly or via JVs by untaxed institutional investors)

Market values: value is based on transactions when possible, but on appraisals or estimates in most cases

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Historical evidence, 1970-2003

Total Return Volatility Risk Premium

T Bills 6.30% 2.83% NAG Bonds 9.74% 11.76% 3.44%Real Estate* 9.91% 9.02%

3.61%Stocks 12.72% 17.48% 6.42%

*NCREIF: large, institutional quality commercial properties

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Quarterly returns on NPI index

1978 1981 1984 1987 1990 1993 1996 1999 2002 2005 2008

-10.00%

-8.00%

-6.00%

-4.00%

-2.00%

0.00%

2.00%

4.00%

6.00%

8.00%

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Value of $1 reinvestment: 1969-2003

$0

$5

$10

$15

$20

$25

$30

$35

$40

$45

$50

69 71 73 75 77 79 81 83 85 87 89 91 93 95 97 99 01 03

CPI TBill SP500 LGBond RE

Stocks $38.04NCREIF 22.18LT Bond 19.63TBills 7.89CPI 4.88

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Survey evidence

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0%

2%

4%

6%

8%

10%

12%

14%

*Source: Korpacz Investor Survey, 1st quarter 2005

Exh.11-6a: Investor Total Return Expectations (IRR) for Various Property Types*

Institutional 9.27% 9.35% 9.28% 9.31% 9.56% 10.03% 10.58% 9.11%

Non-institutional 12.53% 11.00% 10.81% 10.80% 11.68% 12.05% 13.19% 10.38%

MallsStrip Ctrs

Indust. AptsCBD

OfficeSuburb.

Off.Hou.Off

Manh Off

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Capitalization rate approach

Cap rate = (current NOI or PBTCF) / Property Value

Assume current PBTCF cap rate is y, and that we expect PBTCF to grow at rate g for ever

Then IRR on property is r ≈ y + g

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Survey evidence (!! on NOI cap rates !!)

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0%

2%

4%

6%

8%

10%

12%

*Source: Korpacz Investor Survey, 1st quarter 2005

Exh.11-6b: Investor Cap Rate Expectations for Various Property Types*

Institutional 7.33% 7.86% 7.88% 6.74% 8.26% 8.63% 9.19% 7.45%

Non-institutional 10.51% 9.50% 9.02% 8.00% 10.38% 10.18% 11.44% 8.59%

MallsStrip Ctrs

Indust. AptsCBD

OfficeSuburb.

Off.Hou.Off

Manh Off

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Asset pricing models

Find the average unlevered equity beta of similar properties, using, presumably, REITs or NCREIF data

Invoke CAPM to calculate required return on equity

Calculate WACC

Discount

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Multiple/Ratio approach

Find a group of peer properties on which good value data is available due to recent transaction, or rock-solid appraisal

Alternatively, collect/purchase info on appropriate multiples

Apply Cap rate and GRM approach to current property

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When does the multiple approach work?

When comparable properties don’t just have the same y, but also when they have the same g

Outside of fixed g world, we need comparable properties to be roughly scaled up or down version of the target property

Heroic, but standard, and a good way to frame an argument over value

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Debt and taxes

Many investors are subject to taxes at the property level, which matters greatly for value

Two ways to deal properly with the effects of debt and taxes:1. Discount after tax cash flows at after tax WACC2. Discount flows-to-equity (EATCF) at the required rate of

equity

First approach yields the property’s total value, the second one yields the value of equity in the property

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Leverage refresher1. Leverage raises expected returns to equity if and only

if the expected unlevered return exceeds the cost of debt

2. Leverage raises the variance and the “beta” of equity returns provided debt payments are not too risky

3. In a perfect world, leverage would not affect value (MM)

4. In the world we live in, leverage affects value by reducing tax liabilities (+), raising bankruptcy risks (-), disciplining magagers (+)…

Page 75: Erwan Quintin Wisconsin School of Business

Calculating taxes and flows-to-equity

Taxable income = NOI – Depreciation – Interest expenses

Income taxes = Taxable income x Tax rate

ATCF= PBTCF – Income taxes

EATCF=ATCF – Debt service payments

Page 76: Erwan Quintin Wisconsin School of Business

Depreciation Value of property= Value of Land + Value of

Structures and Equipment

Land cannot be depreciated

Depreciable cost basis < Value of the property

Depreciation rates and methods vary for different items

Buildings: 27.5 years straight-line (residential, US) 39 years (non-residential, US)

Page 77: Erwan Quintin Wisconsin School of Business

Calculating reversion cash flows

Capital gains = Net sale proceeds – Adjusted basis

Adjusted basis= Original basis + (Total CAPEX – Depreciation)

Capital gains tax = Capital gains x relevant tax rate

It is also proper to show a final debt payment in a pro-forma table (even though, in principle, it could be folded into standard debt service line)

Page 78: Erwan Quintin Wisconsin School of Business

Capital Gains Tax

Capital gains = (Net sale price – (Original basis +Capex)) + Depreciation

The two pieces are taxed differently

Net sale proceeds – (Original Basis+Capex) is taxed at the capital gains tax rate

Depreciation is taxed at the “depreciation recapture tax rate”, which is typically higher

Page 79: Erwan Quintin Wisconsin School of Business

Example

Net sale price=$1,000,000, Original Basis=$800,000, CAPEX=$100,000, Depreciation=$50,000

Capital gains tax: 15%, Recapture Tax: 25%

CGT = (1,000,000 – 800,000 -100,000) x 0.15 + (50,000) x 0.25

= 27,500

Page 80: Erwan Quintin Wisconsin School of Business

Calculating reversion cash flows

EATCF (reversion) = Net Sale Price – Loan Balance - CGT

Page 81: Erwan Quintin Wisconsin School of Business

And we’re done

Discount ATCF at WACC, or EATCF at required return on equity

One should do an obvious set of multiple calculations too, but in practice it is seldom done

Key point: leverage can make a deal worth it, or kill it, depending on the direct and indirect costs of debt

Page 82: Erwan Quintin Wisconsin School of Business

EATCF from operations

Exhibit 14-1a: Equity After-Tax Cash Flows from Operations PGI - vacancy = EGI

- OEs =NOI Cash Flow Taxes - Capital Improvements Exp. Net Operating Income (NOI) = PBTCF -Interest (I) - Debt Service (Int. & Principal) -Depreciation expense (DE) - Income Tax = Taxable Income = EATCF x Investor’s income tax rate

= Income Tax Due

Page 83: Erwan Quintin Wisconsin School of Business

Exhibit 14-2: Example After-Tax Income & Cash Flow Proformas . . .

Property Purchase Price (Year 0): $1,000,000 Unlevered: Levered:Depreciable Cost Basis: $800,000 Before-tax IRR: 6.04% 7.40%Ordinary Income Tax Rate: 35.00% After-tax IRR: 4.34% 6.44%Capital Gains Tax Rate: 15.00% Ratio AT/BT: 0.719 0.870Depreciation Recapture Rate:____________________25.00% ____________________________________________________________________________________________________________________________________________________________________________________________________________________________

Year: Oper. Reversion Rever. TotalOperating: 1 2 3 4 5 6 7 8 9 Yr.10 Item: Yr.10 Yr.10Accrual Items:

NOI $60,000 $60,600 $61,206 $61,818 $62,436 $63,061 $63,691 $64,328 $64,971 $65,621 Sale Price $1,104,622- Depr.Exp. $29,091 $29,091 $29,091 $29,091 $29,091 $29,091 $29,091 $29,091 $29,091 $29,091 - Book Val $809,091

- Int.Exp. $41,250 $41,140 $41,030 $40,920 $40,810 $40,700 $40,590 $40,480 $40,370 $40,260=Net Income (BT) ($10,341) ($9,631) ($8,915) ($8,193) ($7,465) ($6,730) ($5,990) ($5,243) ($4,490) ($3,730)=Book Gain $295,531 $291,801

- IncTax ($3,619) ($3,371) ($3,120) ($2,867) ($2,613) ($2,356) ($2,096) ($1,835) ($1,571) ($1,305) - CGT $73,421=Net Income (AT) ($6,722) ($6,260) ($5,795) ($5,325) ($4,852) ($4,375) ($3,893) ($3,408) ($2,918) ($2,424) =Gain (AT) $222,111 $219,686

Adjusting Accrual to Reflect Cash Flow:- Cap. Imprv. Expdtr. $0 $0 $50,000 $0 $0 $0 $0 $50,000 $0 $0

+ Depr.Exp. $29,091 $29,091 $29,091 $29,091 $29,091 $29,091 $29,091 $29,091 $29,091 $29,091 + Book Val $809,091-DebtAmort $2,000 $2,000 $2,000 $2,000 $2,000 $2,000 $2,000 $2,000 $2,000 $2,000 -LoanBal $730,000

=EATCF $20,369 $20,831 ($28,704) $21,766 $22,239 $22,716 $23,198 ($26,317) $24,173 $24,667 =EATCF $301,202 $325,868

+ IncTax ($3,619) ($3,371) ($3,120) ($2,867) ($2,613) ($2,356) ($2,096) ($1,835) ($1,571) ($1,305) + CGT $73,421=EBTCF $16,750 $17,460 ($31,824) $18,898 $19,626 $20,361 $21,101 ($28,152) $22,601 $23,361 =EBTCF $374,622 $397,983

________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________CASH FLOW COMPONENTS FORMAT

Year: Oper. Reversion Rever. TotalOperating: 1 2 3 4 5 6 7 8 9 Yr.10 Item Yr.10 Yr.10Accrual Items:

NOI $60,000 $60,600 $61,206 $61,818 $62,436 $63,061 $63,691 $64,328 $64,971 $65,621 Sale Price $1,104,622- Cap. Imprv. Expdtr. $0 $0 $50,000 $0 $0 $0 $0 $50,000 $0 $0

=PBTCF $60,000 $60,600 $11,206 $61,818 $62,436 $63,061 $63,691 $14,328 $64,971 $65,621 =PBTCF $1,104,622 $1,170,243- Debt Svc $43,250 $43,140 $43,030 $42,920 $42,810 $42,700 $42,590 $42,480 $42,370 $42,260 - LoanBal $730,000

=EBTCF $16,750 $17,460 ($31,824) $18,898 $19,626 $20,361 $21,101 ($28,152) $22,601 $23,361 =EBTCF $374,622 $397,983-taxNOI $21,000 $21,210 $21,422 $21,636 $21,853 $22,071 $22,292 $22,515 $22,740 $22,967 taxMktGain $693 $23,661+ DTS $10,182 $10,182 $10,182 $10,182 $10,182 $10,182 $10,182 $10,182 $10,182 $10,182 - AccDTS ($72,727) ($62,545)+ ITS $14,438 $14,399 $14,361 $14,322 $14,284 $14,245 $14,207 $14,168 $14,130 $14,091 $14,091

=EATCF $20,369 $20,831 ($28,704) $21,766 $22,239 $22,716 $23,198 ($26,317) $24,173 $24,667 EATCF $301,202 $325,868

Page 84: Erwan Quintin Wisconsin School of Business

Cash flow components (operations)

Cash Flows to Equity: PBTCF - Loan Debt Service

= EBTCF- Taxes if no DTS or ITS+ DTS+ ITS= EATCF

PATCF: PBTCF - Taxes if no DTS or ITS

+ DTS = PATCF - Loan Debt Service + ITS = EATCF

Page 85: Erwan Quintin Wisconsin School of Business

Apprec.Rate = 1.00% Bldg.Val/Prop.Val= 80.00% Loan= $750,000Yield = 6.00% Depreciable Life= 27.5 years Int= 5.50%Income Tax Rate = 35.00% CGTax Rate = 15.00% Amort/yr $2,000

DepRecapture Rate= 25.00%(1) (2) (3) (4) (5) (6) (7) (8) (9) (10) (11) (12) (13)

tax w/out (4)-(5)+(6) Loan (4)-(9) (7)-(9)+(10) (9)-(10)Year Prop.Val NOI CI PBTCF shields DTS PATCF LoanBal DS ITS EBTCF EATCF LoanATCFs

0 $1,000,000 ($1,000,000) ($1,000,000) $750,000 ($750,000) ($250,000) ($250,000) ($750,000)1 $1,010,000 $60,000 $0 $60,000 $21,000 $10,182 $49,182 $748,000 $43,250 $14,438 $16,750 $20,369 $28,8132 $1,020,100 $60,600 $0 $60,600 $21,210 $10,182 $49,572 $746,000 $43,140 $14,399 $17,460 $20,831 $28,7413 $1,030,301 $61,206 $50,000 $11,206 $21,422 $10,182 ($34) $744,000 $43,030 $14,361 ($31,824) ($28,704) $28,6704 $1,040,604 $61,818 $0 $61,818 $21,636 $10,182 $50,364 $742,000 $42,920 $14,322 $18,898 $21,766 $28,5985 $1,051,010 $62,436 $0 $62,436 $21,853 $10,182 $50,765 $740,000 $42,810 $14,284 $19,626 $22,239 $28,5276 $1,061,520 $63,061 $0 $63,061 $22,071 $10,182 $51,171 $738,000 $42,700 $14,245 $20,361 $22,716 $28,4557 $1,072,135 $63,691 $0 $63,691 $22,292 $10,182 $51,581 $736,000 $42,590 $14,207 $21,101 $23,198 $28,3848 $1,082,857 $64,328 $50,000 $14,328 $22,515 $10,182 $1,995 $734,000 $42,480 $14,168 ($28,152) ($26,317) $28,3129 $1,093,685 $64,971 $0 $64,971 $22,740 $10,182 $52,413 $732,000 $42,370 $14,130 $22,601 $24,173 $28,241

10 $1,104,622 $65,621 $0 $1,170,243 $23,661 ($62,545) $1,084,037 $730,000 $772,260 $14,091 $397,983 $325,868 $758,169

IRR of above CF Stream = 6.04% 4.34% 5.50% 7.40% 6.44% 3.58%

Breaking it down

Page 86: Erwan Quintin Wisconsin School of Business

Cash flow components (reversion)

Cash Flows to Equity: Net Sale Price - Loan Debt Service

= EBTCF- Taxes if no DTS+ DTS (-)= EATCF

PATCF = PBTCF – Taxes if no DTS

+ DTS (-) = PATCF - Loan Debt Service = EATCF

Page 87: Erwan Quintin Wisconsin School of Business

Projected IRR calculations

10-yr Going-in IRR:

  Property (Unlvd) Equity (Levd)

Before-tax 6.04% 7.40%

After-tax 4.34% 6.44%

AT/BT 434/604 = 72% 644/740 = 87%

Effective Tax RateWith ord inc=35%, CGT=15%, Recapt=25%.

 100% – 72% =

28%

 100% - 87% =

13%

Page 88: Erwan Quintin Wisconsin School of Business

A puzzle

Assume that deal is a zero NPV deal for this investor (investor is marginal)

That is: E(rE) = IRR on EATCF at $250,000 cost = 6.44%

By the same logic, expected return on unlevered equity would seem to be: E(rU) = IRR on PATCF at $1,000,000= 4.34%

But rD=5.5% > E(rU)

If MM holds: E(rE)= E(rU)+ ((1-τ) D/E) (E(rU)-rD) < E(rU)

Page 89: Erwan Quintin Wisconsin School of Business

What’s going on?

IRR on PATCF at $1,000,000 is not E(rU)

If the investor is willing to pay $1,000,000 with some debt financing, she would not be willing to pay the same if constrained to go all-equity

In other words E(rU)> IRR on PATCF at $1,000,000

Can we tell what E(rU) is?

Page 90: Erwan Quintin Wisconsin School of Business

Value additivity principle

NPV of investment = PV(ATCF) – Property Price (MV)

= NPV of investment if 100% equity financed + NPV of financing

= NPV(Property) + NPV(Financing)

= Adjusted Present Value (APV)

= [PV(PATCF) – MV] + NPV of financing

If the investor is marginal, APV=0

Market value (MV) of an asset is the value to marginal investor

Page 91: Erwan Quintin Wisconsin School of Business

Investment value

Investment value: IV = MV + APV

I V can exceed MV for some investors because:1. their tax rate is lower than that of marginal investors2. they have access to better/more financing3. they can squeeze more CFs out of the property4. they have some private information about PBTCF

prospects5. …

Investors whose IV>MV are called intramarginal !!!! Doesn’t mean they should pay above MV !!!!

Page 92: Erwan Quintin Wisconsin School of Business

What is E(ru)?

Assume that the investor in exhibit 14.2 is marginal at $1,000,000 (i.e. E(rE) = IRR on EATCF at $250,000)

We have: APV = 0= NPV(Property) + NPV(Financing)= PV(PATCF) – MV + PV(ITS)

It follows that PV(PATCF)= MV-PV(ITS)

We know MV, we know all PATCF, E(ru) is the discount rate in PV(PATCF)

If we can calculate PV(ITS), we will know E(ru)

Page 93: Erwan Quintin Wisconsin School of Business

Discount rates

ITS is highly correlated with debt service flows (perfectly so, in fact, for IOMs)

The natural discount rate for ITS is the rate of interest on debt

In earlier example, if investor is marginal, this implies E(ru)=5.77% (see excel file), which is bigger than rD

Why is it bigger than 4.34%? Why is it lower than 6.44%?

Page 94: Erwan Quintin Wisconsin School of Business

What is the implicit average tax rate?

If Modigliani-Miller is roughly right, then: E(rE)= E(rU)+ ((1-τ) D/E) (E(rU)-rD)

We know E(rE)=6.44% in previous example, while D/E=750/250=3, and (E(rU)-rD)=.27%

Given E(ru), the average tax rate consistent with MM formula is τ=17% (roughly)

Tax rate seems low

Page 95: Erwan Quintin Wisconsin School of Business

A word about the global property market

The largest global investors are institutional (pension funds, sovereign funds, insurance companies…)

Institutionally investable RE is estimated to be around $16trn (1.5 US GDP)

Institutions are loath to invest RE directly because it is illiquid, lumpy, requires careful monitoring…

Instead, they invest via listed (reits) and unlisted (funds) vehicles Funds can be open-ended (allow investment and redemption) or closed-

ended (funds are raised once and for all and deployed for a fixed period of time)

Funds are classified as core, core-plus, value-added and opportunistic The fund model worked well until 2008, but has been under pressure

since then Investors are asking for more control and more manager investment What will the new fund model look like? Read Baum and Hartzell (2011) for more